[aliromman]

This gives a finite scalar completion of the Braverman-He PG(2,9) code on a precisely stated dirty-input subspace. Nine independent junk values can pass through the transcript as matched input pairs while all 157 messages remain intact; the included correction restores those nine junk values. This is a local scalar capability, with no physical supplier or verified kappa improvement.

Proof and interface, completion receipt, correction matrices, independent agent review, and source pins.

Over F3[t]/(t^2+1), replacing the former zero C stubs by independent inputs gives an invertible 175-by-175 transfer M=[[I157,F],[G,H]]. The off-diagonal blocks have rank nine; H and the Schur matrix H-GF have rank 18. This transfer is not a role permutation.

Give both input stubs of each C edge the same value. The message outputs then have no junk term, and the two outputs of each J pair agree. Taking one output per pair gives the 166-input map

(x,z) -> (x,Bx+Dz),  with D invertible of size 9.

Applying D^-1 to the junk and subtracting D^-1 Bx gives the identity. All 166 formal GF9 columns are checked. Arbitrary independent values on the 18 C stubs do not satisfy this contract: a nonzero contamination witness is retained in the review. Selecting one matched output is not free erasure of an additional arbitrary borrowed register.

The correction has rank nine and 1,243 nonzero coefficients. The transcript has 735 network transmissions. These are matrix and network counts, not recursive paid costs. Matched-input preparation, duplicate-output handling, legal rational frames, correction access, physical return, hosting, recursive children, and a complex companion remain open.

From the repository root, with Python 3.10+ and its standard library:

python3 -B research/pg29-matched-dirty-completion/verify.py

Expected final line:

PASS_PG29_DIRTY_PACKAGE independent_stubs=175 matched_inputs=166 no_new_kappa

Two separate field implementations replayed all 182 local invertible maps, 735 transmissions, and boundary coefficients. The completion check also compared every saved correction factor. The independent agent review also checked the arithmetic through 2-by-2 matrices over F3 and verified all 332 lifted identity columns. A changed correction factor and a singular local map were rejected. The separate matrix check confirmed that omitting the correction or normalization fails. The wrapper passed with both PYTHONOPTIMIZE=1 and -O. The pinned primary verifier and historical generator regenerated the transcript byte-for-byte; that is provenance corroboration, not an independent derivation of the projective geometry. No Lean, full supplier, outer kappa calculation, or hosted CI pass is claimed.

Base: cef4b52f2a59009865bf8eabde1be3f159063703. Mark Braverman and Zhongtian He supplied the code in arXiv:2610.10108v1, section 4 and the companion source at 3436359a. The new package retains a mathematical transcript and separately written replay code; it does not redistribute that companion implementation. The physical sign-gauge obstruction in PR #288, with the explicit witness in PR #349, is related work and is not resolved here.

Prepared by Ali Romman with substantial OpenAI Codex assistance and separate agent review, not independent human review. New work is Apache-2.0. The next construction obligation is stated in the package: realize the matched injection and correction at legal frames, with arbitrary dirt restored and every recursive child charged.

[jwr404]

Independent review at head 234d173341b2683b4076982ce9da98d0e6362736

Scope. I replayed dirty-word.json from scratch and checked every algebraic claim in PROOF.md. The replay code is my own:

• GF(9) is represented as a + b·i over F3, with inverses taken through the norm. No field code is shared with independent_dirty.py or completion.py.
• Local words are scheduled by a worklist, so file order is not trusted. The scheduler also asserts acyclicity and that every internal packet is produced exactly once.

All claims reproduce.

Claim	Independent result
182 local 5×5 maps invertible	✓
Physical transmissions	735, each packet produced once. The file order is already topological (one scheduling round).
Transfer equals saved transfer	✓
rank M	175, with top-left block I_157
rank F, G, H	9, 9, 18
Schur H − GF	rank 18, so invertible
C pairs / J pairs	edges {102, 163, 164, 341, 386, 406, 476, 513, 862} / {103, 349, 470, 517, 603, 606, 674, 716, 861}
FP = 0; G and HP rows agree within each J pair	✓
D = QHP	invertible, 74 nonzeros
D⁻¹B	rank 9, 1,243 nonzeros
All 166 matched formal columns restored to the identity by (x, Bx+Dz) ↦ (x, z)	✓
Saved B9, D9, inverse_D9 and correction equal my B, D, D⁻¹ and D⁻¹B	✓ entrywise
Unmatched C inputs contaminate messages (F ≠ 0)	✓, consistent with the stated limitation

Scope notes. None blocks the PR.

• This verifies the finite algebra given the transcript. Whether dirty-word.json faithfully encodes Braverman–He PG(2,9), with the former zero C stubs freed, is provenance: the package's byte-for-byte regeneration from the pinned historical generator. I did not re-derive the projective-plane code.
• The PR already states correctly that matched-input preparation, duplicate-output handling, frames and costs are open, and that 735 is not a paid profile.

This is an author-independent check. It is not maintainer acceptance, and κ is unchanged.

Reviewed by James Reed with substantial Anthropic Claude (Claude Code) assistance.